Simplify the following expression: $ p = \dfrac{3}{10} + \dfrac{-2k - 9}{-2k + 7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-2k + 7}{-2k + 7}$ $ \dfrac{3}{10} \times \dfrac{-2k + 7}{-2k + 7} = \dfrac{-6k + 21}{-20k + 70} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-2k - 9}{-2k + 7} \times \dfrac{10}{10} = \dfrac{-20k - 90}{-20k + 70} $ Therefore $ p = \dfrac{-6k + 21}{-20k + 70} + \dfrac{-20k - 90}{-20k + 70} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{-6k + 21 - 20k - 90}{-20k + 70} $ $p = \dfrac{-26k - 69}{-20k + 70}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{26k + 69}{20k - 70}$